This includes graphs of start parameters including chamber pressure (MCC PC).

Thrust is roughly proportional to PC. A thrust curve isn't shown in this paper, but here's a simplified one from my notes from working on the engine model in the Shuttle Mission Simulator. Units are lbf on the vertical axis, seconds on the horizontal.

Edit: Just noticed you asked about flowrates too. Again from SMS SSME model notes, here are simplified plots of the startup flowrates. Red is LO2, blue is LH2, Y axis units are lbm/sec.